THE MOONS OF MARS

1 OVERVIEW

Mars has two moons, Phobos and Deimos, that are both very
small and irregular in shape. They orbit quite close to the
planet, and Phobos, the inner and larger moon, has the
distinction of being the only natural satellite in the solar
system that orbits its planet in less time than it takes the
planet to rotate about its axis.

Phobos - NASA Viking Orbiter

Because of their small size, they were discovered only a
little over a century ago. They are both very dark objects,
covered in craters and possibly many metres of fine
dust. However, strangest of all is the apparent knowledge of
their existence 150 years before they were discovered!

2 DISCOVERY

The English Astronomer William Herschal made an unsuccessful
search for satellites of Mars in 1783. His renown was such
that many astronomers were thereby convinced that Mars had no
moons.

A very careful search was conducted in 1864 at the Copenhagen
Observatory by H L d'Arrest. However, he was no more
succesful than was Herschal. It was not until 1877 that the
two moons of Mars were discovered by Asaph Hall at the US
Naval Observatory in Washington DC, USA. The outer satellite
was discovered on August 11th and the inner one on August
17th. The telecope used by Hall for his discoveries was a 26-
inch refractor.

3 NAMING

In the words of Asaph Hall, "Of the various names that have
been proposed for these satellites, I have chosen those
suggested by Mr Madan of Eton, England, viz: Deimos for the
outer satellite; Phobos for the inner satellite. These are
generally the names of the horses that draw the chariot of
Mars; but in the lines referred to [in the 15th book of the
Iliad] they are personified by Homer, and mean the attendants,
or sons of Mars {the god of war}."

The Greek word phobos means fear. The English word phobia is
derived from this. Deimos is translated terror, or sometimes
flight. It is thus easy to remember the order of these moons.
Phobos is the inner moon, Deimos the outer. When fear is
close, flight takes you further away.

4 DESCRIPTION

The moons of Mars are so small that no detail can be seen with
an Earth based telescope. It was not until 1971 that the US
Mariner 9 spacecraft obtained the first images to show surface
detail. Both moons are irregular in shape, and have surfaces
that are pockmarked by many craters.

Phobos is the larger of the two moons and is roughly an
ellipsoid 19.2 x 21.4 x 27.0 km across its 3 axes. Deimos is
about 11 x 12 x 15 km.

Deimos
Viking 1 Orbiter
NASA

Phobos orbiting above Mars
Image from Russian
Phobos 2 spacecraft

The surface of Phobos shows many sharp, uneroded craters of
all sizes together with a vast network of linear features.
These grooves are many kilometres long and hundreds of metres
wide. They appear to be surface fractures associated with a
very large (in comparison to the moon) crater called Stickney.
This crater is 10 km in diameter and it dominates the moon's
topography.

Both moons have crater densities comparable to the lunar
uplands, and this suggests an age of a few billion years for
each body.

5 ORIGIN

The irregular shapes of the moons and their heavy cratering
shows that they have had a history of collisions and possibly
fragmentation with other bodies.

Several theories have been proposed for their origin. One
belief is that these moons are asteroids that have been
gravitationally captured by Mars. Another is that they are
fragments of an original larger Martian satellite that was
struck and fragmented by an asteroid, the other pieces having
escaped the Martian gravitational field. It appears unlikely
that they could have simply grown from an orderly accumulation
of many small grains of an original solar nebulae.

Sample return missions from both Mars and its moons are needed
to resolve this issue.

6 ORBITS

Both moons orbit quite close to Mars. Phobos, in fact, lies
just outside the Roche limit (that radius below which a
gravitational-adhesive bound body may break up due to tidal
forces induced by the primary). It is believed that there may
well be significant internal movements of Phobos caused by
tidal forces exerted on the moon by Mars. These could be
measured by a seismometer placed on the surface.

The orbital parameters are given in the table below:

Parameter

PHOBOS

DEIMOS

Semimajor axis (km)

9380

23500

Mean altitude (km)

6000

20000

Sidereal period (hours)

7.65

30.3

Orbit eccentricity

0.018

0.002

Orbit inclination (deg)

1.0

2.0

Rotational period (hr)

7.65

30.3

We might note that the very low orbital eccentricity means
that both moons have almost circular orbits. They also orbit
very close to the equatorial plane of Mars (by contrast, the
Earth's moon has an inclination that varies from 18 to 29
degrees).

In the table above, the mean altitude is the average distance
of the moon above the Martian surface. The sidereal period is
the time that it takes the moon to complete a revolution of
360 degrees in space (to come back to the same point with
respect to the stars). This is not the time between two
successive moonrises (see section 8).

It is interesting to examine a table showing the period
(sidereal) of a Martian orbital satellite with orbital radius:

*MARS Orbiting Satellites*

Height

Velocity

Period

(km)

(km/s)

(mins)

450

3.3

120.4 [Mars Global Surveyor orbit]

1000

3.13

147.2

3000

2.59

258.3

6000

2.14

460.0 [Orbit of Phobos]

9000

1.86

697.2

12000

1.67

965.0

15000

1.53

1260.5

17000

1.45

1471.6 [Areosynchronous orbit period = 1477.4 mins]

20000

1.36

1807.9 [Orbit of Deimos]

Areosynchronous orbit is the Martian analog of geosynchronous
orbit. This is the orbit that a spacecraft would need to
remain stationary over a given point on the Martian equator.
Because this orbit is close to that of the moon Deimos,
satellite controllers may have a more difficult job than their
terrestrial counterparts in station keeping communication and
other satellites in this orbit (due to gravitational
perturbations from Deimos). Fortunately the small mass of the
moon will minimise such effects.

Both moons have rotation periods that are locked to their
orbital motion. This means they continually present the same
face to Mars (as our Moon does to the Earth). The long axis
of each moon points toward Mars. This is due to gravity
gradient stabilisation (the same phenomenon is sometimes used
to stabilize low Earth orbiting satellites - using a long
"gravity gradient" boom).

And finally, it is now known that the orbit of Phobos is slowly
decaying - coming closer to Mars - and its expected lifetime is
about 50 million years. Atmospheric drag should
make the last part of its de-orbit fairly rapid.

7 PROPERTIES

Not a great deal is known about the properties of these two
small moons. For several decades the Viking Orbiters provided the
best images of the martian moons. However, recent missions such as
the US Mars Global Surveyor and the European Mars Express have
added both images and data to our knowledge.

Phobos as seen by the European Space Agency
Mars Express mission. Craters cover the surface of
the moon, some with diameters that are substantial
fractions of the moon's size. The largest crater is
called Stickney.

ESA image

The surfaces of both Phobos and Deimos are very dark. This is
seen by examining the albedo of several planets and moons in
the solar system.

BODY

ALBEDO

Mercury

0.10

Venus

0.586

Earth

0.39

Mars

0.15

Jupiter

0.44

Saturn

0.46

Uranus

0.56

BODY

ALBEDO

Moon

0.115

Phobos

0.06

Deimos

0.06

Io

0.92

Europa

0.83

Ganymede

0.49

Callisto

0.26

This (visual geometric) albedo is a measure of the surface
reflectivity of the object. A value of 0 would mean a totally
black surface, and a value of 1 would indicate that all the
light incident on the object is reflected back.

Of all the planets, Venus has the highest albedo due to its
cloud cover. Phobos and Deimos, on the other hand are the
darkest bodies (with the exception of some asteroids) in the
solar system. It is no wonder they were so hard to find!

The low albedo is probably due both to the composition - it is
believed that both moons are similar to carbonaceous chondrite
meteorites - and the pulverisation of this material by
countless surface meteoroid impacts. The regolith (surface
covering rock) may consist of a good depth of fine carbon-like
material.

The table below gives estimated masses, and average surface
gravities.

Parameter

PHOBOS

DEIMOS

Mass of moon (kg)

9.6E15

2.0E15

Density (kg/m^3)

1900

2100

Mean radius (km)

11

6

Surface gravity (m/s/s)

0.005

0.004 (g/Earth=9.8)

Escape velocity (km/hr)

40

25

We can thus see that the surface gravity is less than 1/1000
that of Earth. The escape velocity, particularly on Deimos
would be low enough for an athletic person to achieve, and
even normal activities could propel you into space, and you
would be a long time returning back to the moon!

8 THE VIEW FROM MARS

It is not the sidereal period of a satellite, but its synodic
period that is important when observing from the planet's
surface. This is the time between two successive appearances
of the moon at the same place in the sky (for example between
successive moonrises or moonsets). For Phobos this time is
11.1 hours. Thus you would see two moonrises and two moonsets
on most Martian days (sometimes you may see three). Because
this moon is below Areosynchronous orbit, it will rise in the
west and set in the east.

Deimos moves much more slowly in the sky. Because it is just
above Areosynchronous orbit, it has a period only a few hours
longer than the rotational period of Mars. It will rise in
the east, move slowly across the sky and set in the west a
little over 2.5 days latter. It will rise again in 5.5 days,
its synodic period.

Even though the moons of Mars are much closer to their primary
(ie Mars) than is our Moon to the Earth, their small size
still makes them appear smaller in the Martian sky than does
the Moon in our sky. When overhead, Phobos subtends an angle
of 11 minutes of arc which is only about one third of the Moon
as seen from Earth. Another difference is that this angle
varies as Phobos moves across the sky. When rising or
setting, this moon subtends only 8 minutes of arc to an
observer on the equator. This is a 30% reduction in the size
it shows at the zenith. It is interesting to speculate that
because of the pyschological illusion of increased size near
the horizons (where the eye has a reference of comparison),
the physical size reduction may go largely unnoticed.

In this image taken by the Mars Exploration Rover
'Spirit' from the surface of Mars, Phobos and Deimos
are seen in the night sky close to one another, illustrating
their relative brightness.

NASA/JPL image

Deimos, which is not only smaller physically, but also further
away, will appear as barely more than a bright star with an
angular diameter of 2 minutes of arc when overhead at the
equator. This is only twice the angle subtended by Venus at
its closest approach to Earth. The variation in size as
Deimos moves across the sky will be rather smaller than for
Phobos.

The irregular shape of Phobos will be clearly apparent from
Mars, but that of Deimos may be barely noticed. That is,
Phobos will clearly be non-circular, but Deimos will barely be
perceived as a disk with no visible structure.

The fact that both moons have very low inclination orbits
means that they will not be visible from higher latitudes.
Phobos will not be visible at latitudes above about 70
degrees, nor Deimos above about 83 degrees.

The low inclination of the moon orbits also means that they
will often pass into the shadow of Mars. Such moon eclipses
will occur about 1400 times for Phobos and 130 times for
Deimos each Martian year (about 687 Earth days). There are
also a similar number of solar transits each year. Neither
moon subtends a large enough angle to eclipse the sun, even
though the sun subtends a smaller angle from Mars than it does
from the Earth. The sun appears about two thirds of the size
it does from Earth (21 minutes of arc). Phobos appears about
one half this size and Deimos about one tenth.

Two eclipse images taken by the Mars Exploration Rover
'Spirit' from the surface of Mars, show the size of the two
moons relative to the Sun.

NASA/JPL image

9 A MYSTERY?

In 1726 the British author Jonathon Swift wrote a satirical
book called 'Gulliver's Travels'. In this work, Swift wrote
that the inhabitants of Laputa had discovered two satellites
that revolve around Mars. Not content with this, Swift even
specified the orbital radius and periods of these moons as
follows:

Inner Moon

Outer Moon

(Swift) /

(Actual)

(Swift) /

(Actual)

Radius (Mars Diameters)

3

1.38

5

3.46

Revolution period (hrs)

10

7.7

21.5

30.3

Many people have been astounded by Swift's apparent knowledge
of these Martian moons 150 years before they were discovered
by Asaph Hall. It is particularly interesting why Swift
should have placed the inner moon so close to the planet, with
such an unusually fast period of revolution.

However, as amazing as this may seem at first glance, a
detailed analysis shows that Swift's choices are quite in
accord with the available scientific knowledge of the day.

In 1610, following Galileo's discovery of 4 moons around
Jupiter, Kepler speculated that Mars would be found to have 2
moons. He based this on observations that in proceeding out
from the Sun, Venus had no moons, Earth one, Mars two, the
"missing" planet three, and Jupiter four. This belief would
have been strengthened in Swift's time, as by then five moons
had been discovered around Saturn.

If we look at the orbital radii of the moons of Jupiter, we
might see why Swift chose the orbits he did for the Martian
moons.

*Orbital radii of Jovian Moons in Jovian diameters*

Moon 1 (Io)

2.9 (rounds to Swift's value of 3)

Moon 2 (Europa)

4.7 (rounds to Swift's value of 5)

Moon 3 (Ganymede)

7.4 (N/A)

Moon 4 (Callisto)

13.1 (N/A)

Once the orbital radius is given then Kepler's or Newton's
laws may be called upon to compute the period. Two quantities
are needed for this calculation - the diameter of Mars and its
mass (or alternatively Kepler's constant for Mars). The first
quantity was known (although it was believed to be 7700 km).
It appears that Swift assumed an Earth mass, as this gives the
figures he quoted. And so we see that maybe the "mystery" is
not so mysterious after all. Some people have stated that
Swift could not possibly have performed the required
calculations. This may be so. But he undoubtedly had friends
who could!